{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FVM Backward Facing Step\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/mesh/FVM_BackStep.ipynb)\n",
    "\n",
    "This example shows how to run a finite volumes incompressible fluid simulation on an unstructured mesh."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install --quiet phiflow\n",
    "from phi.jax.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
    "from tqdm.notebook import trange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "obstacle = Box(x=.5, y=.5)\n",
    "vert_x = concat([\n",
    "    math.linspace(0, .4, spatial(x=20))[:-1],\n",
    "    math.linspace(.4, .6, spatial(x=20))[:-1],\n",
    "    math.linspace(.6, 1, spatial(x=20)),\n",
    "    ], 'x')\n",
    "vert_y = math.linspace(0, 1, spatial(y=31))\n",
    "mesh = geom.build_mesh(x=vert_x, y=vert_y, obstacles=obstacle)\n",
    "plot(mesh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit_compile_linear\n",
    "def momentum_eq(u, u_prev, dt, diffusivity=0.01):\n",
    "    diffusion_term = dt * diffuse.differential(u, diffusivity, correct_skew=False)\n",
    "    advection_term = dt * advect.differential(u, u_prev, order=1)\n",
    "    return u + advection_term + diffusion_term\n",
    "\n",
    "@jit_compile\n",
    "def implicit_time_step(v, dt):\n",
    "    v = math.solve_linear(momentum_eq, v, Solve(x0=v), u_prev=v, dt=-dt)\n",
    "    v, p = fluid.make_incompressible(v)\n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b87fdfe98f25460e9253e52e407103f3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boundary = {'x-': vec(x=.1, y=0), 'obstacle': 0, 'y': 0, 'x+': ZERO_GRADIENT}\n",
    "velocity = Field(mesh, tensor(vec(x=0, y=0)), boundary)\n",
    "v_trj = math.iterate(implicit_time_step, batch(time=100), velocity, dt=0.01, range=trange)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x186ab1c3130>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(v_trj, v_trj.to_grid(), animate='time')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "phiflow2",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
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